It especially tends to break online payment solutions, I've had more than one purchase go haywire, including one where I just got the "order confirmed!" page instantly, without ever entering any payment details. Their support guy was a little bit confused about that one ;-)
So now I put my trust in the block lists, Privacy Possum, Decentraleyes and Firefox' built-in fingerprinting resistance function ("privacy.resistFingerprinting" in about:config).
The latest additions are Multi-Account Containers and Temporary Containers. Every new site opens in a sandboxed temporary container that gets deleted 15 minutes after I close the last tab in it. This discards all cookies, cache, everything stored about that site, except browsing history entries. Think of it as a cookie autodelete on steroids. I have permanent containers set up for sites where I want to store the login or other information, such as HN or FB. Each site can only see its own container, so there's no cross-site tracking.